Oxygen does not have a bond order of 3, it should have a bond order of two unless it's O22+. Since the 1s and 2s MOs are filled, only the 2p MOs will be used in determining the bond order. Note that all 3 of the 2p bonding orbitals -- sigma gerade, pi ungerade (x), and pi ungerade (y) -- are filled completely. Note also that both of the pi gerade antibonding orbitals contain one electron each. 6 bonding electrons - 2 antibonding electrons = 4 and so 4/2 = 2 = bond order.
g and u do not mean bonding and antibonding. They have to do with the symmetry of the orbitals. If the orbital changes sign upon inversion through the center of the molecule, the symmetry is ungerade. If the orbital does not change sign, the symmetry is gerade. Pictures would really help here. g and u can however help you deduce whether the orbital is bonding or antibonding.
K does mean what you think it means.
The x, y, z subscripts indicate spatial orientations of the orbitals. Usually the bond axis is referred to as the z-axis. This is why you see a sigma bonding orbital with a z subscript.
L does mean what you think it means. It's just shorthand.
In the P2 example, the 4 electrons is another kind of shorthand. It is understood that the p orbitals in the x and y directions are degenerate so they combined them into one term representing 2 orbitals. There are no antibonding electrons in this example (hint).
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Topic: Ground-state electron configuration (Read 13465 times)